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A267644 T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row and column unequal to the previous repeated value, and new values introduced in row-major sequential order.

%I A267644 #4 Jan 18 2016 20:12:36
%S A267644 1,2,2,3,8,3,5,18,18,5,7,50,51,50,7,11,98,189,189,98,11,15,242,429,
%T A267644 1015,429,242,15,23,450,1353,2887,2887,1353,450,23,31,1058,2829,12623,
%U A267644 8917,12623,2829,1058,31,47,1922,8427,32303,47715,47715,32303,8427,1922,47,63
%N A267644 T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row and column unequal to the previous repeated value, and new values introduced in row-major sequential order.
%C A267644 Table starts
%C A267644 ..1....2.....3.......5.......7........11........15..........23..........31
%C A267644 ..2....8....18......50......98.......242.......450........1058........1922
%C A267644 ..3...18....51.....189.....429......1353......2829........8427.......16899
%C A267644 ..5...50...189....1015....2887.....12623.....32303......131673......319541
%C A267644 ..7...98...429....2887....8917.....47715....128441......647101.....1614281
%C A267644 .11..242..1353...12623...47715....343145...1117207.....7479533....22499181
%C A267644 .15..450..2829...32303..128441...1117207...3696933....30649693....90914453
%C A267644 .23.1058..8427..131673..647101...7479533..30649693...330654951..1225925501
%C A267644 .31.1922.16899..319541.1614281..22499181..90914453..1225925501..4301737251
%C A267644 .47.4418.49443.1277029.8168679.150415627.784186403.13431652713.62439362175
%H A267644 R. H. Hardin, <a href="/A267644/b267644.txt">Table of n, a(n) for n = 1..220</a>
%F A267644 Empirical for column k:
%F A267644 k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
%F A267644 k=2: a(n) = a(n-1) +6*a(n-2) -6*a(n-3) -8*a(n-4) +8*a(n-5)
%F A267644 k=3: [order 11]
%F A267644 k=4: [order 35]
%F A267644 k=5: [order 93]
%e A267644 Some solutions for n=5 k=4
%e A267644 ..0..1..0..1....0..1..0..0....0..1..0..0....0..1..0..0....0..1..0..1
%e A267644 ..0..0..1..0....1..0..1..0....1..0..1..1....1..1..0..0....1..0..1..0
%e A267644 ..1..1..0..1....1..0..0..1....0..1..0..0....0..0..1..1....0..1..1..0
%e A267644 ..1..0..0..1....0..1..1..0....1..0..1..0....0..1..0..0....1..0..0..1
%e A267644 ..0..0..1..0....0..1..0..1....0..1..0..1....1..0..1..1....1..1..0..0
%Y A267644 Column 1 is A052955(n-1).
%K A267644 nonn,tabl
%O A267644 1,2
%A A267644 _R. H. Hardin_, Jan 18 2016